2017 AMC 8 第 9 题
先试着解答 2017 AMC 8 第 9 题，然后核对你的答案与视频与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2017 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
9.
玛茜的所有弹珠都是蓝色、红色、绿色或黄色。她的弹珠中三分之一是蓝色，四分之一是红色，且有六颗绿色弹珠。玛茜最少可能有多少颗黄色弹珠？
All of Marcy’s marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Marcy could have?
小提示：
弹珠总数必须同时能被 和 整除
The total number of marbles must be divisible by both and .
大提示：
测试最小的 的倍数，直到能容纳 颗绿色弹珠
Test the smallest multiples of until there is room for the green marbles.
视频讲解：
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文字解答：
如果弹珠总数同时能被 和 整除，那么它必须能被 整除。测试 时，蓝色有 颗，红色有 颗，最多只剩 颗绿色，不可能。
若总数为 ，则蓝色有 颗，红色有 颗。黄色弹珠数为 。
所以正确答案是 D。
If the number of marbles is divisible by both and then the number must be divisible by If we test we get that there are blue marbles and red marbles. This leaves a maximum of green marbles, which is not possible.
If there are marbles, then there are blue marbles and red marbles. To find the number of yellow marbles, we get
Thus, D is the correct answer.
其他年份的第 9 题
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- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
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